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Resonance-assisted tunneling in four-dimensional normal-form Hamiltonians
Markus Firmbach1,2, Felix Fritzsch1, Roland Ketzmerick1,2
1Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany.
Physical Review. E
|May 22, 2019
Summary
Nonlinear resonances significantly enhance quantum tunneling. Double resonances create complex tunneling peak structures in four-dimensional Hamiltonian systems, explained by normal-form Hamiltonians and perturbative methods.
Area of Science:
- Quantum mechanics
- Classical mechanics
- Chaos theory
Background:
- Nonlinear resonances in classical phase space are known to enhance quantum tunneling.
- Understanding tunneling phenomena is crucial in various quantum systems.
Purpose of the Study:
- To investigate the effect of double resonances on tunneling peak structures.
- To explain the underlying mechanisms of tunneling enhancement and suppression.
Main Methods:
- Utilizing the universal description of resonances via four-dimensional normal-form Hamiltonians.
- Applying perturbative methods to analyze resonance effects.
- Employing a minimal matrix model for intuitive understanding.
Main Results:
- Demonstrated that double resonances lead to complicated tunneling peak structures.
- Revealed the mechanism behind tunneling enhancement and suppression with excellent quantitative agreement.
- Obtained an intuitive understanding of the phenomenon through a minimal matrix model.
Conclusions:
- Nonlinear resonances, particularly double resonances, play a critical role in shaping quantum tunneling.
- The study provides a robust theoretical framework for understanding complex tunneling phenomena in multidimensional Hamiltonian systems.
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